M4459369 Mersenne number exponent details

Residue

Status

L-L

471E1E85A501FC77

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	6.6633	65.6716%	1800000	68000000	0.9778	8.2052%	7.6411	68.4883%	2.8167%
PrimeNet	2⁶¹	0.0689	62.2951%	18000	360000	0.0066	2.9443%	0.0755	63.4052%	1.1101%
GPU72	2⁶⁵	1.6360	64.6154%	26000	550000	0.0099	2.0877%	1.6459	65.3541%	0.7387%
Difference	+2	+5.0272	+1.0563%	+1774000	+67450000	+0.9679	+6.1175%	+5.9952	+3.1342%	+3.1342%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.6633

65.6716%

1800000

68000000

0.9778

8.2052%

7.6411

68.4883%

2.8167%

PrimeNet

2⁶¹

0.0689

62.2951%

18000

360000

0.0066

2.9443%

0.0755

63.4052%

1.1101%

GPU72

2⁶⁵

1.6360

64.6154%

26000

550000

0.0099

2.0877%

1.6459

65.3541%

0.7387%

Difference

+5.0272

+1.0563%

+1774000

+67450000

+0.9679

+6.1175%

+5.9952

+3.1342%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4459369	7460230275388200829597714406863	31	102.557	836467028786830696181199 3³ × 7 × 13 × 19 × 43 × 1451 × 6221 × 8689 × 5312809	2016-12-14	8689	5312809	3.396e+10	0.0538	0.0978

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4459369

7460230275388200829597714406863

102.557

836467028786830696181199
3³ × 7 × 13 × 19 × 43 × 1451 × 6221 × 8689 × 5312809

2016-12-14

8689

5312809

3.396e+10

0.0538

0.0978

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-03-11T00:00:00	ANONYMOUS	v4_computers	20000	145000		-		-	-	0.005	-	-	0.978%
2010-08-28T14:39:00	markr	tiny	95000	2090000		-		-	-	0.037	-	-	2.974%
2016-12-14T11:10:36	mikr	MSI	1800000	68000000	12		7460230275388200829597714406863	31	102.557	0.978	1.112	1.956	8.205%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-06-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-
2010-10-12T09:48:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.069	-	-
2012-02-03T03:49:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.358	-	-
2016-02-23T16:38:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.220	-	-
2014-09-17T20:21:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.440	-	-
2014-09-18T20:42:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.838	-	-
2015-06-24T23:36:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.676	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.660 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.660 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.660

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-03-08T05:38:00	oodaira	Linux01	50000	5000000						3	0.553
2013-04-24T01:07:00	S00030	mac399	50000	5000000						3	0.553
2016-09-29T23:54:08	S04803	lfmcal	50000	5000000						3	0.553

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-16T00:00:00	Phillip Remaker	v4_computers	2AB2110A41B786__	0.556
2000-01-25T00:00:00	akohler	v4_computers	471E1E85A501FC77	0.556
2001-04-21T00:00:00	ANONYMOUS	v4_computers	471E1E85A501FC77	0.556

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-17T00:59:45

kkmrkkblmbrbk

c4.xlarge

7460230275388200829597714406863

AB3221ED4AFB62__

2018-02-15T04:08:49

Oliver Kruse

GTX-6

7460230275388200829597714406863

AB3221ED4AFB62__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1800000, B2 = 68000000 (P-1 stage 2)

B1 = 1800000 (P-1 stage 1)

B1 = 95000, B2 = 2090000 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 20000, B2 = 145000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront